In this work, we study the estimation of water-quality parameters from the water-leaving reflectance by means of spectral unmixing. Our starting point is the provision of an analytic model relating the reflectance of water to its masses/bodies or constituents, as specified by their specific inherent optical properties (SIOP) and concentrations. The main objective is to reformulate the estimation of these concentrations as a spectral unmixing problem. We perform this by employing the linear mixing model (LMM), while suitably defining the endmembers (EMs) as representations of different water types dominated by one or more constituents. Each EM is then calculated by substituting the in situ-measured SIOP and combinations of utmost concentrations of each constituent into the water-reflectance model. Such use of unmixing practically enables to maintain an implicitly nonlinear relation between the water reflectance and constituents' concentrations, without resorting to the use of nonlinear mixing models. Furthermore, we present a method to automatically extract the EMs from the reflectance image. We validate the entire unmixing-based take using the state-of-the-art method as reference that inverts the water reflectance via comparisons (curve matching) with spectra from a lookup table. This validation is done using simulated data derived from the water-reflectance model and real hyperspectral data acquired over coastal waters of a shallow sea.